3D Sketch Problem

Problem: Sketch by hand the graph of the plane 2x + 4y + z = 8. Draw the circle of radius one lying on
the plane and centered at (1, 1, 2). What is the radius of the largest circle lying on the plane and
centered at (1, 1, 2) that is wholly contained in the ﬁrst octant? Explain.

My answer:
I found the intercepts (4,0,0) , (0,2,0) , (0,0,8)
Then I sketched the plane in the first octant.
Completely lost with finding the largest circle.

Problem: Sketch by hand the graph of the plane 2x + 4y + z = 8. Draw the circle of radius one lying on
the plane and centered at (1, 1, 2). What is the radius of the largest circle lying on the plane and
centered at (1, 1, 2) that is wholly contained in the ﬁrst octant? Explain.

My answer:
I found the intercepts (4,0,0) , (0,2,0) , (0,0,8)
Then I sketched the plane in the first octant.
Completely lost with finding the largest circle.

I hope this reply doesn't come too late ...

1. You have determined the intercepts
P(4,0,0), Q(0,2,0) and R(0,0,8)

2. The lines PQ, QR and PR must be tangents to the circle in question. The radius is the perpendicular distance of the center C(1,1,2) to a line.

3. Calculate the 3 perpendicular distances. The shortest of these distances is the greatest radius such that the circle is placed completely in the first octant.